Why Do CPO Lead to Slow Light When the Laser

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Why Do CPO Lead to Slow Light When the
Laser Linewidth Exceeds the Width of the CPO
Transparency Window?
Giovanni Piredda and Robert W. Boyd University
of Rochester
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Coherent Population Oscillations
The technique of Coherent Population Oscillations
(CPO) allows control of the velocity of light.
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CPO in a graph
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CPO has been used with modulation bands ranging
from Hz 1 to THz 2. In some of these
experiments, for example in (1), slow light is
observed even if the bandwidth of the laser, on
the order of 1 GHz, is much larger than the width
of the CPO hole (37 Hz). This is possible
because CPO is an effect that is sensitive to
light intensity, not field.
1 M. S. Bigelow et al, PRL 90, 113903
(2003) 2 M. van der Poel et al, Optics Express
13, 8032 (2005)
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CPO from rate equations
Assume an intensity of the form
and solve using the trial solution
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CPO from rate equations
Neglect second order and collect terms with the
same time dependence the solutions are
Using these solutions we obtain equations for I0
(the pump) and I1 (the modulation)
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CPO from rate equations
In the equation for I1 two features appear a dip
in the absorption (the CPO hole) a phase shift of
the modulation The phase shift leads to the slow
light effect it is related to the group velocity
of light, because I1 represents a modulation
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The comparison with experimental results is
excellent
Figures from M. S. Bigelow et al, PRL 90, 113903
(2003)
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CPO with non-collinear pump and signal
The delay that can be achieved using CPO is
limited by pump absorption in order to reach
large fractional delays it is necessary that the
pump intensity is uniform along the propagation
direction of the signal. A way to achieve this is
to let pump and signal propagate in different
directions
Pei-Cheng Ku et al., OL 29, 2291 Su and Chuang,
OL 31, 271
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CPO with non-collinear pump and signal
The refractive index for the signal beam can be
calculated using the density matrix equation of
motion for the two-level atom
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CPO with non-collinear pump and signal
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CPO with non-collinear pump and signal
The following term appears in the polarization
It represents the scattering of the pump beam off
the population grating created by the beating of
the pump with the signal it influences the
absorption and refractive index of the signal
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CPO with non-collinear pump and signal
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Conclusions
A laser with a 1 GHz bandwidth can burn a 37 Hz
hole because CPO is an effect that is sensitive
only to intensity modulations.
The CPO effect is the same for every angle
between the propagation directions of pump and
signal.
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Acknowledgements
Prof Boyds research group, Aaron Schweinsberg in
particular DARPA and NSF for financial support